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The physics of fast: Why McGrath was faster than you think

Have you ever wondered why the speed gun shows a modest read for bowlers with a high-arm action, such as Glenn McGrath? Fouad Khan offers his insight as to why this is the case

<b>Fouad Khan</b>
Glenn McGrath imitates the pose of a wax statue of himself at Madame Tussauds, Sydney, July 31, 2013

Glenn McGrath demonstrating his high-arm action with his likeness  •  AFP

I recently stumbled upon a forum where an Australian fan had asked rather wistfully if, in the beginning of Glenn McGrath's career, there was a time when he used to be fast. I think this is a false question. For all the talk of McGrath being the metronome, the impeccable line and length, and the consistency, one feature that I can't shake off is his ability to rush the batsman. Yet, for much of the last three quarters of his career, when speed guns truly became ubiquitous, McGrath seemed to be trundling in between low to mid 130s kph. What was at play here?
Turns out the answer to this question is very simple if we discuss the physics of pace in a little more depth. What I am about to describe is not cutting edge science, but the application of basic mechanics to fast bowling, especially in regards to bowling speed. I am actually surprised nobody has done this before, considering that the physics used here is elementary compared to what the University of Western Australia uses to analyse hyper flexible joints and reverse swing.
Have you ever noticed a thoroughbred fast bowler, say Brett Lee, run in and let loose a fierce bouncer that the batsman and his three immediate ancestors had no clue about, only to have the speed gun report a comparatively modest speed of 88 mph? How many times have you heard the commentator go, "Well, I'm sure it looked a lot quicker from the batsman's end?" One empirically, rather well-realised (though not statistically established) fact of fast bowling is that bouncers are slower than yorkers. The reason bouncers are slower is that the speed gun measures speed. Human perception, on the other hand, is looking at "velocity"; a slightly different thing. Speed is a scalar quantity; velocity is a vector. Speed can be fully expressed using one measurement. Velocity is meaningless without also mentioning direction.
When a fast bowler releases the ball, the ball travels in a three-dimensional space. Just as the distance covered by the ball is in three dimensions, the velocity of the ball, which is distance divided by time, is also in three dimensions. The distance covered by the ball can be said to have three components: the distance covered towards the batsman, the distance covered towards and away from the pitch surface, and the distance covered laterally due to any lateral movement, or the angle of the delivery.
Similarly, the velocity of the ball can be said to have the same three components at any given time. By defining these three "axes" we have defined a Cartesian frame of reference for analysing the movement of the ball through space. Since these three components of distance and velocity are at right angles to one another, we can find the total distance covered by the ball, as well as the total velocity, by summing the squares of each of the components, and then taking the square root of the sum.
The key thing to understand is that the velocity of the ball has three components. The speed gun only measures one of these components, which is the component of the velocity towards the batsman. The speed reported by the speed gun is only a measure of how long or short it took the ball to reach the batsman once it was released. This is not a good measure as the batsman and bowler are not in a straight line in respect to the speed gun, and doesn't account for lateral movement.
McGrath was fast because the vertical component of the velocity of his deliveries - the speed of the ball towards and away from the pitch - was very high. This vertical velocity manifests itself in "nip". Bowlers for whom this velocity is high are usually considered to have nip. Nip does not register on the speed gun. In fact, the higher the nip, the lower the other components of the velocity of the delivery will be, because there is only so much velocity a bowler can impart on a ball. This is why bouncers are usually slower on the speed gun compared to yorkers. The component of the velocity directed towards the batsman - and most accurately represented by the speed gun - can be called "skid". A skiddy bowler is someone who seems to rush on to the batsmen.
A convenient way to imagine the difference between skid and nip is to assess how much distance, in a certain axis, the ball travels. Velocity is equal to distance divided by time. The higher the distance covered, the higher the velocity. Imagine McGrath now, releasing the ball from a height of about 7.5ft. The vertical component, towards the pitch and away, of the distance covered would be 7.5ft, plus the height at which the ball passed the batsman, say 4ft. The total distance would therefore be more than 11 feet.
Compare that with Malinga releasing the ball at say 5.5ft, and making contact at 2ft, giving a total distance of 7ft. Since the (vertical) distance covered by McGrath's delivery was much higher, the vertical velocity or "nip" of McGrath's delivery would be higher. However, Malinga's delivery took a shorter amount of time to get to the batsman, partly because it didn't have to cover all that vertical distance, and went directly for the kill. The component of velocity towards the batsman (skid) would be higher as velocity is inversely proportional to time taken. This is why Malinga would be faster on the speed gun.
But just because the speed gun cannot measure nip does not mean humans don't perceive it. Plenty of batsmen would attest to the fact that they perceived McGrath's nip all right, even if it didn't register on the speed gun. So now we know that McGrath was indeed fast, just not in a way that could be measured by a speed gun. This also explains why bouncers are usually slower on the speed gun compared to other types of deliveries covering less ground vertically. This is why "slingers" like Malinga and Fidel Edwards tend to register higher speeds on the speed gun compared to bowlers releasing the ball from greater heights, such as Glenn McGrath or Stuart Clark.